Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C79×#1413 ⋊ C2 |
| Sylow | C79 ⋊ #7525 |
138 conjugacy classes of subgroups; only the 25 normal subgroups are shown.
This group has 138 conjugacy classes of subgroups — too many to draw. Only its 25 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 111 |
| transitive degree | μt(G) = 2528 |
A minimal faithful permutation representation — 2 generators on 111 points:
(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21)(22,23)(24,25)(26,27)(28,29)(30,31)(32,33)(34,35)(36,37)(38,39)(40,41)(42,43)(44,45)(46,47)(48,49)(50,51)(52,53)(54,55)(56,57)(58,59)(60,61)(62,63)(64,65)(66,67)(68,69)(70,71)(72,73)(74,75)(76,77)(78,79)(81,86)(82,91)(85,97)(87,103)(88,101)(89,102)(90,107)(94,109)(96,99)(100,106)(104,111)(105,110);(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,54,56,58,60,62,64,66,68,70,72,74,76,78,79,77,75,73,71,69,67,65,63,61,59,57,55,53,51,49,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5,3)(80,81,83,87,84,89,95,105)(82,90,92,103,91,101,108,110)(85,88,99,106,97,107,96,104)(86,94,100,98,102,109,111,93)Polycyclic presentation:
2^8,79|a^2=d,c^2=g,d^2=h,e^2=gh,f^2=h,b^a=bc,c^a=ce,e^a=ef,f^a=fg,g^a=gh,c^b=cg,d^b=deh,e^b=egh,f^b=fg,i^b=i^78,d^c=dfg,e^c=eg,f^c=fh,e^d=egh,f^d=fh565 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 57413);